1. 12.10 Relative-Motion Analysis of Two Particles Using Translating Axes
Relative Motion (Translating Axes)
- Consider two particles A and B. Both are moving with respect to fixed axes X-Y
- The translating axes x-y is moving with particle B
- The position vector of the particle A measured relative to the x-y axes is
(A/B means A with respect to B)

2. KINEMATICS OF PARTICLES
If is the absolute position of B, then
Take derivative with respect to time : or
and or

4. A B
160 km/h
180 km/h

5. EXAMPLE
The passenger aircraft B is flying east with velocity vB = 800 km/h. A jet is traveling south with velocity vA = 1200 km/h. What velocity does A appear to a passenger in B ? x y
Solution

6. EXAMPLE (Cont.)
Absolute value :
The direction of y
West of South x

7. Example q

8. Example

9. Problem
At the instant shown, the car at A is traveling at 10 m/s around the curve while increasing its speed at 2 m/s2. The car at B is traveling at 18.5 m/s along the straightway and increasing its speed at 5 m/s2. Determine the relative velocity and relative acceleration of A with respect to B at this instant

10. Thank you